Mon, 20 July, 2009, 09:00-10:00, C1
The motivation for tomographic examinations is to get information on the internal structures of the scanned object, either a human being in medical imaging or a work piece in non-destructive testing. So far the information was presented in form of series of images, and the task then was to extract the searched-for features. As a first step often image enhancement methods are applied, disregarding the reconstruction procedure. In edge detection for example the image is again smoothed and then differentiated.
The aim of this presentation is to provide a general strategy for optimally combining these two steps of image reconstruction and image enhancement in just one procedure, leading to very efficient algorithms. The theoretical background is formulated for abstract inverse problems and the application of linear operators on the reconstructed objects. To this end, the reconstruction kernel in the approximate inverse is modified depending on the desired features and the smoothing properties of the involved operators. Suitable invariance properties preserve the efficiency of the reconstruction algorithm for computing the features.
As example we discuss x-ray tomography in two and three dimensions combined with edge detection, smoothing for very noisy data and finally for the calculation of wavelet coefficients of the object. Numerical results are presented for synthetic and for measured data.
Presentation slides (pdf, 1.8 MB)
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